The minimum energy required to launch a satellite of mass m from the surface of earth of radius R in a cirulcar orbit at an altitude 2R is (mass of earth is M)

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Solution

The correct option is D.
Energy of the satellite on the surface of earth is only the potential energy given by.

$E_{i} = - \frac{G m M}{R}$
The energy of satellite at a distance (2R + R) = 3R from center of earth is both potential as well as kinetic. Hence the total energy is given by,

$E_{f} = - \frac{G m M}{2 (3 R)} = - \frac{G M m}{6 R}$

$∴$ Energy required to launch the satellite is

E = $E_{f} - E_{i} = - \frac{G M m}{6 R} - (- \frac{G m M}{R}) = \frac{5 G M m}{6 R}$ .

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